Question

1st term is 3, last term 136, the sum is 1390, what is the first 3 terms?

Answer 1

`a = 3` and `d = 7`
The sequence is 3, 10, 17 .....

Explanation:

This would appear to be a question on an arithmetic series.

In order to find consecutive terms, we need to find the value of the common difference, `d`

There are two formulae for finding the sum of a series, the one we will need to use is
`S_n = n/2(a+l)`...... we know thw sum as well as the first and the last term, but not how many terms were added.

Substituting and solving for `n` gives the following:

`n/2(a+l) = S_n` `rArr n/2(3+136) = 1390`

`n(139) = 2780)`

`n = 20` ...........................Now we know that 136 is the 20th term.

`T_20 = a + (n-1)d = 136` ..................... `a=1 and n = 20`

`3 + 19d` = `136` `rArr19d = 133`

`d = 7`

Now that we have `a and d` we can write any term in the sequence.